{"id":174472,"date":"2023-10-20T02:58:10","date_gmt":"2023-10-20T07:58:10","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2023\/10\/mobius-mystery-solved-by-mathematician-after-5-decades"},"modified":"2023-10-20T02:58:10","modified_gmt":"2023-10-20T07:58:10","slug":"mobius-mystery-solved-by-mathematician-after-5-decades","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2023\/10\/mobius-mystery-solved-by-mathematician-after-5-decades","title":{"rendered":"M\u00f6bius Mystery Solved By Mathematician After 5 Decades"},"content":{"rendered":"

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M\u00f6bius strips are fun geometrical shapes that only have one side. Take a strip of paper \u2013 it\u2019s got a front and a back. Now twist it and glue the two short edges together. Suddenly there is no front or back. You could draw a line across its whole surface without having to lift the pencil from the paper. Forty-six years ago mathematicians suggested the minimum size for such a strip but they couldn\u2019t prove it. Now, someone finally has.<\/p>\n

Since the creation of the strip by August Ferdinand M\u00f6bius and Johann Benedict Listing, its simplicity in making and visualizing it had to be balanced with the mathematical<\/a> complexity of such a shape. It is not surprising that in 1977, Charles Sidney Weaver and Benjamin Rigler Halpern created the Halpern-Weaver Conjecture, which stated the minimal ratio between the width of the strip and its length. They suggested that for a strip with a width of 1 centimeter (0.39 inches), the length had to be at least the square root of 3 centimeters (about 1.73 centimeters or 0.68 inches).<\/p>\n

For smooth M\u00f6bius strips that are \u201cembedded\u201d, meaning they don\u2019t intersect with each other, the conjecture had no solution. If the strip can go through itself, it is a much easier problem to solve, Brown University\u2019s mathematician Richard Evan Schwartz proposed in 2020 \u2013 but he had made a mistake. In a paper posted as a preprint \u2013 meaning it is yet to be subjected to peer review<\/a> \u2013 Schwartz corrected the error and found the right solution for the conjecture.<\/p>\n","protected":false},"excerpt":{"rendered":"

M\u00f6bius strips are fun geometrical shapes that only have one side. Take a strip of paper \u2013 it\u2019s got a front and a back. Now twist it and glue the two short edges together. Suddenly there is no front or back. You could draw a line across its whole surface without having to lift the [\u2026]<\/p>\n","protected":false},"author":511,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229],"tags":[],"class_list":["post-174472","post","type-post","status-publish","format-standard","hentry","category-mathematics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/174472","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/511"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=174472"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/174472\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=174472"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=174472"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=174472"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}